Most armies in the first quarter of the nineteenth century were issued a wool uniform (regimental) coat worn both for home service and active service. A second garment or drill jacket was often issued that could be described a vest with sleeves, round jacket or for mounted branches as a stable jacket.
The John Jenkins War of 1812 US troops wear a jacket like this in gray wool. The most common material in many armies was white linen or cotton as it could be easily cleaned and was inexpensive to produce.
The appearance in the field would be determined by the availability of replacement clothing which could be from depots or locally procured. This often would include overalls, or trousers in addition to the gaiters and knee breeches.
Rain covers were also available in some armies to prolong the life of the shakos. This headgear was made from sized wool felt, leather with wool binding tape, metal and woolen ornaments. The linen or cotton covers were painted to help repel water and wee slipped over the shako and tied in place.
Some equipment was only issued for campaign such as backpacks, greatcoats, canteens and in some armies haversacks. As garrison troops and for drilling or inspection at depots the men wold normally appear only with cross belts and full regimental uniform coats, gaiters, knee breeches and fully dressed shakos or bearskins.
The 100 days campaign leading up to Waterloo is recorded as having a wild variety of clothing worn in the French army and allows great latitude within reason.
As far as unit integrity for British units, although small units might be brigaded together, the various units would remain together by section, or platoon and these platoons would form a company.
If you are new to collecting and wish to display your troops in a diorama setting I would advise you to concentrate of one unit and build some numbers that would include enlisted men, NCOs, company officers and musicians. In the British army of the period flags, or Colours would be carried by the Battalion or Center Companies and not by the flank companies like Grenadiers or Lights.
This is only the tip of the iceberg, but I hope it helps a bit,
Ken